Propagation of electromagnetic waves in stochastic helical media

Abstract

We have developed a model for studying the axial propagation of elliptically polarized electromagnetic waves in a spatially random helical media. We start by writing Maxwell equations for a structurally chiral medium whose dielectric permittivities, polar, and helical angles contain both a stochastic contribution and a deterministic one. We write the electromagnetic equations into a Marcuvitz-Schwigner representation to transform them afterward in a simpler expression by using the Oseen transformation. We exhibit that in the Oseen frame the Marcuvitz-Schwigner equations turns out to be a linear vector stochastic system of differential equations with multiplicative noise. Applying to the resulting equation a formalism for treating stochastic differential equations, we find the governing equations for the first moments of the electromagnetic field amplitudes for a general autocorrelation function for the system diffractive indexes, and calculate their corresponding band structure for a particular spectral noise density. We have shown that the average resulting electromagnetic fields exhibit a decaying exponential dependence which stems from by dissipation and the presence of qualitative modifications in the band structure including a considerable widening of the band gap and the existence of new local maxima for the modes without a band gap.